Generating narrow-band spectral images from broad-band spectral images

ABSTRACT

System and method for narrowing the transmission curves obtained using a spectral imager in which spectral images are acquired using a MEMS Fabri-Perot (FP) tunable filter. A method includes acquiring a first plurality of broad-band spectral images associated with respective MEMS FP etalon states and processing the first plurality of broad-band spectral images into a second plurality of narrow-band spectral images.

CROSS REFERENCE

This application claims priority from U.S. provisional patent 62/644,538filing date Mar. 18, 2018 which is incorporated herein by its entirety.

BACKGROUND

Small tunable filters include microelectromechanical system (MEMS)filters such as the MEMS Fabri-Perot filter (hereinafter—FP etalon).

There is a growing need to provide narrow band images from a spectralimager that includes a FP etalon.

SUMMARY

There may be provided methods, spectral imagers and computer programproducts for generating narrow-band spectral images from broad-bandspectral images. The generating of narrow-band spectral images from thebroad-band spectral images may include constructing the narrow-bandspectral images by a set of linear transformations applied on thebroad-band spectral images through the use of a reconstruction matrix.

There may be provided a method for generating narrow-band spectralimages, the method may include acquiring, by a spectral imager that mayinclude a tunable filter, a first plurality (N) of broad-band spectralimages associated with respective states of the tunable filter; andprocessing, by a processing circuitry the first plurality of broad-bandspectral images into a second plurality (M) of narrow-band spectralimages.

The reconstruction matrix when multiplied by H, which is a matrix thatrepresents spectral responses associated with respective states of thetunable filter, can result in a sparse matrix which ideally resemblesthe unity matrix associated with an ideal narrow-band (e.g.hyperspectral) filter.

The each broad-band image of the first plurality of broad-band spectralimages may be associated with a respective broad-band transmission curvehaving a respective broad-band full width half maximum value; andwherein each narrow-band spectral image of the second plurality ofnarrow-band spectral images may be associated with a respectivenarrow-band transmission curve having a narrow-band full width halfmaximum smaller than the broad-band full width half maximum value of thebroad-band transmission curve.

The spectral imager may include an image sensor having a filter arraywith a third plurality (C) of filter types, wherein filters of differenttypes differ from each other by transfer function; and wherein C exceedstwo.

C may equal three and the filter array may be a color filter array.

C may equal three and the filter array may be a red, green and bluecolor filter array.

C may equal four and the filter array may be a red, green, blue andinfrared filter array.

C may equal four and the filter array may be a red, green, blue andwhite filter array.

C may equal three and the filter array may be a red, blue and whitefilter array

The method may include applying an expansion process for generating,from the first plurality of broad-band spectral images, a fourthplurality (Q) of broad-band spectral images and processing the fourthplurality of broad-band spectral images into the second plurality of thenarrow-band spectral images; and wherein Q exceeds each one of N and M.

The ratio between Q and N may be an integer.

The expansion process may be a demosaicing process.

The expansion process differs from a demosaicing process.

The processing of the fourth plurality of broad-band spectral imagesinto the second plurality of narrow-band spectral images may includeconstructing the second plurality of narrow-band spectral images bylinearly transforming the fourth plurality of broad-band spectral imagesusing a reconstruction matrix.

The method may include constructing the second plurality of narrow-bandspectral images by using a reconstruction matrix; wherein thereconstruction matrix represents a cost function and spectral responsesassociated with respective states of the tunable filter.

The reconstruction matrix may be calculated based on a Tikhonov matrix.

The Tikhonov matrix may be a multiple of the identity matrix.

The Tikhonov matrix may be a lowpass operator.

The Tikhonov matrix may be selected out of a group of Tikhonov matrices.

The group of Tikhonov matrices may be associated with a group ofreconstruction matrices; wherein different reconstructions matrices ofthe group may be associated with different values of one or morespectral imager performance attributes.

The one or more spectral imager performance attributes may include asignal to noise ratio.

The one or more spectral imager performance attributes may include aresolution.

The reconstruction matrix may equal (H^(T)H+Γ^(T)Γ)⁻¹H^(T), wherein Hmay be a matrix that represents spectral responses associated withrespective states of the tunable filter, and Γ a Tikhonov matrix.

Alternatively, the reconstruction matrix may includeO^(T)H[(H^(T)H+Γ^(T)Γ)⁻¹]^(T) wherein O may be a general matrix.

The method may include selecting the Tikhonov matrix out of a group ofTikhonov matrices.

The selecting may be based on at least one property of at least one ofthe first plurality of broad-band spectral images.

The at least one property may be a signal to noise ratio.

The at least one property may be a resolution.

The method may include calculating the reconstruction matrix.

The cost function may be a Tikhonov matrix.

The Tikhonov matrix may be a multiple of the identity matrix.

The Tikhonov matrix may be a lowpass operator.

The method may include selecting the Tikhonov matrix out of a group ofTikhonov matrices.

The group of Tikhonov matrices may be associated with a group ofreconstruction matrices; wherein different reconstructions matrices ofthe group may be associated with different values of one or morespectral imager performance attributes.

The one or more spectral imager performance attributes may include asignal to noise ratio.

The one or more spectral imager performance attributes may include aresolution.

The reconstruction matrix may equal (H^(T)H+Γ^(T)Γ)⁻¹H^(T), wherein Hmay be a matrix that represents spectral responses associated withrespective states of the tunable filter, and Γ a Tikhonov matrix.

Alternatively, the reconstruction matrix may includeO^(T)H[(H^(T)H+Γ^(T)Γ)⁻¹]^(T), wherein O may be a general matrix.

The image sensor may be a monochromatic image sensor.

The tunable filter may be a Fabri Perot etalon.

The tunable filter may be a single Fabri Perot etalon that operates,when acquiring the first plurality of broad-band spectral images in awavelength range of 400-1000 nanometers.

The method further may include displaying one or more of the Mnarrow-band spectral images.

There may be provided a spectral imager that may include a tunablefilter and a sensor; wherein the sensor may be configured to acquire afirst plurality (N) of broad-band spectral images associated withrespective states of the tunable filter; and

a processing circuitry that may be configured to process the firstplurality of broad-band spectral images into a second plurality (M) ofnarrow-band spectral images.

Each broad-band image of the first plurality of broad-band spectralimages may be associated with a respective broad-band transmission curvehaving a respective broad-band full width half maximum value; andwherein each narrow-band spectral image of the second plurality ofnarrow-band spectral images may be associated with a respectivenarrow-band transmission curve having a narrow-band full width halfmaximum smaller than the broad-band full width half maximum value of thebroad-band transmission curve.

The spectral imager may include an image sensor having a filter arraywith a third plurality (C) of filter types, wherein filters of differenttypes differ from each other by transfer function; and wherein C exceedstwo.

C may equal three and the filter array may be a color filter array.

C may equal three and the filter array may be a red, green and bluecolor filter array.

C may equal four and the filter array may be a red, green, blue andinfrared filter array.

C may equal four and the filter array may be a red, green, blue andwhite filter array.

C may equal three and the filter array may be a red, blue and whitefilter array

The processing circuitry may be configured to apply an expansion processfor generating, from the first plurality of broad-band spectral images,a fourth plurality (Q) of broad-band spectral images and process thefourth plurality of broad-band spectral images into the second pluralityof the narrow-band spectral images; and wherein Q exceeds each one of Nand M.

The ratio between Q and N may be an integer.

The expansion process may be a demosaicing process.

The expansion process differs from a demosaicing process.

The processing circuitry may be configured to construct the secondplurality of narrow-band spectral images by linearly transforming thefourth plurality of broad-band spectral images using a reconstructionmatrix.

The processing circuitry may be configured to construct the secondplurality of narrow-band spectral images by using a reconstructionmatrix; wherein the reconstruction matrix represents a cost function andspectral responses associated with respective states of the tunablefilter.

The reconstruction matrix may be calculated based on a Tikhonov matrix.

The Tikhonov matrix may be a multiple of the identity matrix.

The Tikhonov matrix may be a lowpass operator.

The Tikhonov matrix may be selected out of a group of Tikhonov matrices.

The group of Tikhonov matrices may be associated with a group ofreconstruction matrices; wherein different reconstructions matrices ofthe group may be associated with different values of one or morespectral imager performance attributes.

The one or more spectral imager performance attributes may include asignal to noise ratio.

The one or more spectral imager performance attributes may include aresolution.

The reconstruction matrix may equal (H^(T)H+Γ^(T)Γ)⁻¹H^(T), wherein Hmay be a matrix that represents spectral responses associated withrespective states of the tunable filter, and Γ a Tikhonov matrix.

Alternatively, the reconstruction matrix may includeO^(T)H[(H^(T)H+Γ^(T)Γ)⁻¹]^(T), wherein O may be a general matrix.

The Processing circuitry may be configured to perform a selection of theTikhonov matrix out of a group of Tikhonov matrices.

The selection may be responsive to at least one property of at least oneof the first plurality of broad-band spectral images.

The at least one property may be a signal to noise ratio.

The at least one property may be a resolution.

The processing circuitry may be configured to calculate thereconstruction matrix.

The cost function may be a Tikhonov matrix.

The Tikhonov matrix may be a multiple of the identity matrix.

The Tikhonov matrix may be a lowpass operator.

The processing circuitry may be configured to select the Tikhonov matrixout of a group of Tikhonov matrices.

The group of Tikhonov matrices may be associated with a group ofreconstruction matrices; wherein different reconstructions matrices ofthe group may be associated with different values of one or morespectral imager performance attributes.

The one or more spectral imager performance attributes may include asignal to noise ratio.

The one or more spectral imager performance attributes may include aresolution.

The reconstruction matrix may equal (H^(T)H+Γ^(T)Γ)⁻¹H^(T), wherein Hmay be a matrix that represents spectral responses associated withrespective states of the tunable filter, and Γ a Tikhonov matrix.

Alternatively, the reconstruction matrix may includeO^(T)H[(H^(T)H+Γ^(T)Γ)⁻¹]^(T) wherein O may be a general matrix.

The image sensor may be a monochromatic image sensor.

The tunable filter may be a Fabri Perot etalon.

The tunable filter may be a single Fabri Perot etalon that operates,when acquiring the first plurality of broad-band spectral images in awavelength range of 400-1000 nanometers.

There may be provided a method for generating narrow-band spectralimages, the method may include: acquiring, by a spectral imager that mayinclude a tunable light source, a first plurality (N) of broad-bandspectral images associated with respective states of the tunable lightsource; and processing, by a processing circuitry the first plurality ofbroad-band spectral images into a second plurality (M) of narrow-bandspectral images.

There may be provided a method for generating narrow-band spectralimages, the method may include: receiving by a processing circuitry, afirst plurality (N) of broad-band spectral images; wherein the Nbroad-band spectral images were acquired by a spectral imager that mayinclude a tunable filter; wherein the N broad-band spectral images maybe associated with respective states of the tunable filter; andprocessing, by the processing circuitry, the first plurality ofbroad-band spectral images into a second plurality (M) of narrow-bandspectral images.

There may be provided a method for generating narrow-band spectralimages, the method may include: receiving by a processing circuitry, afirst plurality (N) of broad-band spectral images; wherein the Nbroad-band spectral images were acquired by a spectral imager that mayinclude a tunable filter; wherein the N broad-band spectral images maybe associated with respective states of the tunable filter; andprocessing, by the processing circuitry, the first plurality ofbroad-band spectral images into a second plurality (M) of narrow-bandspectral images.

There may be provided a non-transitory computer readable medium thatstores instructions that once executed by a processing circuitry causesthe processing circuitry to receive a first plurality (N) of broad-bandspectral images; wherein the N broad-band spectral images were acquiredby a spectral imager that may include a tunable filter; wherein the Nbroad-band spectral images may be associated with respective states ofthe tunable filter; and process the first plurality of broad-bandspectral images into a second plurality (M) of narrow-band spectralimages.

There may be provided a non-transitory computer readable medium thatstores instructions that once executed by a device that may include aspectral imager and a processing circuitry causes the device to acquire,by a spectral imager that may include a tunable filter, a firstplurality (N) of broad-band spectral images associated with respectivestates of the tunable filter; and process, by the processing circuitrythe first plurality of broad-band spectral images into a secondplurality (M) of narrow-band spectral images.

BRIEF DESCRIPTION OF THE DRAWINGS

Non-limiting examples of embodiments disclosed herein are describedbelow with reference to figures attached hereto that are listedfollowing this paragraph. The drawings and descriptions are meant toilluminate and clarify embodiments disclosed herein and should not beconsidered limiting in any way. Like elements in different drawings maybe indicated by like numerals.

FIG. 1 illustrates schematically a known spectral imaging system basedon operation of a FP etalon;

FIG. 2A shows one half of a broad-band system response obtained atdifferent states of operation of a FP etalon based spectral imagingsystem disclosed herein;

FIG. 2B shows another half of a broad-band system response obtained atdifferent states of operation of a FP etalon based spectral imagingsystem disclosed herein;

FIG. 3 shows schematically in a flow chart two general steps of a methoddisclosed herein;

FIG. 4A shows schematically in a flow chart more details of a methoddisclosed herein, for a FP etalon based spectral imager with a colorimage sensor;

FIG. 4B shows schematically in a flow chart more details of a methoddisclosed herein, for a FP etalon based spectral imager with amonochromatic image sensor;

FIG. 5A shows one third of a total system response obtained afterapplying a method disclosed herein to the broad-band system response ofFIGS. 2A and 2B;

FIG. 5B shows another third of a total system response obtained afterapplying a method disclosed herein to the broad-band system response ofFIGS. 2A and 2B;

FIG. 5C shows yet another third of a total system response obtainedafter applying a method disclosed herein to the broad-band systemresponse of FIGS. 2A and 2B;

FIG. 6 illustrates an example of a method;

FIG. 7 illustrates an example of a method;

FIG. 8A illustrates an example of a system in which a tunable filter isplaced between the object and the image sensor;

FIG. 8B illustrates an example of a system in which a tunable filter isplaced in front of a light source which illuminates the object; and

FIG. 8C illustrates an example of a system in which a first tunablefilter is placed in front of a light source which illuminates the objectand a second tunable filter is placed between the object and the imagesensor.

DETAILED DESCRIPTION

Any reference to a spectral imager should be applied, mutatis mutandisto a method that is executed by a spectral imager and/or to a computerprogram product that stores instructions that once executed by thespectral imager will cause the spectral imager to execute the method.

Any reference to method should be applied, mutatis mutandis to aspectral imager that is configured to execute the method and/or to acomputer program product that stores instructions that once executed bythe spectral imager will cause the spectral imager to execute themethod.

Any reference to a computer program product should be applied, mutatismutandis to a method that is executed by a spectral imager and/or aspectral imager that is configured to execute the instructions stored inthe non-transitory computer readable medium.

The term “and/or” is additionally or alternatively.

A narrow-band FP etalon can be designed (a) either using metallic singlelayer coatings, or (b) using multilayer dielectric coatings.

On one hand, since metallic coatings have a very high absorption, thetransmission of a FP etalon having such filter coatings is practicallytoo low (˜5%). On the other hand, in order to get sufficiently narrowtransmission bands with a multi-layer dielectric coatings design, thenumber of coating layers needs to be high (˜22 layers), leading to athick coating stack that causes very high residual stress on MEMSsubstrates and deforms them mechanically.

Thus, due to the constrains on the total permissible stress in thecoatings, the number of such coating layers on a FP etalon has to besignificantly reduced, inevitably causing the transmission bands tobecome much wider in comparison to those achievable when using thesignificantly thicker substrates commonly used in non-MEMS Fabri-Perotfilters.

To qualify as “hyperspectral”, a tunable filter needs to provide verynarrow-band transmission curves (e.g. with a full width half maximum(FWHM) of 1-10 nm). In practice, very narrow-band FP etalon filters (andin particular MEMS based filters) are limited to work either(approximately) in the 400-600 nm wavelength range or (approximately) inthe 600-900 nm wavelength range, since their transmission curves cannotbe made narrow over a wide wavelength range such as the 400-1000 nmrange without introducing higher order “blobs” in the transmissioncurves.

There is therefore a need for, and it would be desirable to have a MEMSFP etalon-based spectral imagers that provide narrow-bandfilters/transmission curves over a wide (e.g. 400-1000 nm) wavelengthrange.

In the following detailed description, the term “broad-band spectra”refers to spectra resembling that (for example—equal) of a spectrum of asingle band pass filter with a FWHM equal to or greater than apredefined value—such as but not limited to 50 nm, or that of amulti-band pass filter) and the term “narrow-band spectra” refers tospectra resembling (for example—equals) that of a single band passfilter with a FWHM smaller than the predefined value—such as but notlimited to 50 nm). When used, the term “narrower-band spectra” refers tospectra that is narrower than broad band spectra by a FWHM in the rangeof 0-1 nm, 1-10 nm, 10-50 nm, 50-100 nm and even more than 100 nm.

Narrow-band transmission curves and even hyperspectral transmissioncurves may be obtained in an extended wavelength range (e.g. 400-1000nm) using a spectral imager such as the spectral imager of FIG. 1 and byconverting broad-band spectral images to narrow-band spectral images.

Broad-band spectral images can be obtained using a FP etalon thatprovides only broad-band transmission spectra (for example, spectra withFWHM greater than about 75-100 nm). These broad-band spectral images canbe converted using methods and processes disclosed herein intonarrow-band spectral images and even hyperspectral spectral images. Thesuggested methods, spectral imagers and computer program productsprovide a cheap, highly effective (low absorbance) and high resolutionspectral imager.

A FP etalon can be designed such that each of its states produces atransmission curve with a form that resembles that of a multi-bandtransmission filter which partially overlaps the transmission curves ofthe filter's neighboring states. Each state of the FP etalon provides abroad-band spectrum with a given shape, from which one can obtain a“broad-band spectral image” that includes a number of mixed wavelengths.It is disclosed herein that the broad-band spectral image can then betransformed into one or more narrower-band spectral (and evenhyperspectral) images. The transformation may include reconstruction ofan imaged object's radiosity (also referred to as “flux density” and“irradiance” and expressed in Watts/m2) as if obtained with a series ofnarrow-band filters, by manipulating the image data obtained through themulti-band transmission curves.

In an example there is provided a method, that may include providing aspectral imager that includes a FP etalon, acquiring a first plurality(N) of broad-band spectral images associated with respective FP etalonstates, a processing of the first plurality of broad-band spectralimages into a second plurality (M) of narrow-band spectral images. N andM are positive integers.

In an example, each broad-band image of the first plurality isassociated with a respective broad-band transmission curve having arespective broad-band full width half maximum value FWHM_(BB) and eachnarrow-band spectral image of the second plurality is associated with arespective narrow-band transmission curve having a narrow-band fullwidth half maximum FWHM_(NB) smaller than FWHM_(BB).

In an example, the spectral imager includes a color image sensor havinga color filter array (CFA) with a third plurality (C) of filter types.

In an example, C=3, the first plurality includes N broad-band spectralimages Í_(1 . . . N), and the method may include applying an expansionprocess (such as but not limited to demosaicing) to the Í_(1 . . . N)images to obtain A fourth plurality (Q) of broad-band spectral images(for example 3N broad-band spectral images) I_(1 . . . 3N) andprocessing the I_(1 . . . 3N) broad-band spectral images into the secondplurality (M) M≤3N narrow-band spectral images {tilde over(R)}_(1 . . . M).

In an example, C=4, the first plurality includes N broad-band spectralimages Í_(1 . . . N), and the method further comprises applyingdemosaicing to the Í_(1 . . . N) images to obtain 4N broad-band spectralimages I_(1 . . . 4N) and processing the I_(1 . . . 4N) broad-bandspectral images into M≤4N narrow-band spectral images {tilde over(R)}_(1 . . . M).

Yet in another example, the spectral imager includes a monochromaticimage sensor without a CFA, the first plurality of broad-band spectralimages includes N broad-band spectral images Í_(1 . . . N), and themethod further comprises processing the Í_(1 . . . N) broad-bandspectral images into a M≤N narrow-band spectral images {tilde over(R)}_(1 . . . M).

FIG. 1 illustrates an example of a spectral imager that is based on theoperation of a tunable filter such as the FP etalon.

FIG. 1 illustrates a spectral imager 100 that includes an optical unit102 and image sensor 104 and a control system 105.

Control system 105 includes a control unit 106 configured for datacommunication with a readout circuit of image sensor 104 for receivingimage data therefrom and processing the received data.

Optical 102 includes a tunable filter such as a tunable dispersiveunit/element that functions as a wide spectral filter 108.

In an example, the tunable dispersive unit/element is a FP etalon with awide transmission peak. Control unit 106 includes data input and outpututilities (not shown), a memory module 106A and an analyzer module 106Badapted for analyzing the image data from the pixel matrix unit 104.

Control system 105 further includes a controller 107, which isconfigured to control the tuning of FP etalon 108 and to provide dataabout the variation of a tunable parameter. The controller may be partof control unit 106, a separate module, or part of etalon 108.

The tuning of the FP etalon is aimed at controllably varying itsspectral transmission profile (transmission function), i.e. at changingthe dispersive pattern of light passing therethrough. In case of a FPetalon, the tunable parameter of FP etalon 108 is a gap between itsreflective surfaces. Different gaps correspond to different states.

Controller 107 operates the tuning procedure and provides data about thedifferent values of the tunable parameter, e.g. gapi, . . . gapN, orprovides data about the corresponding transmission functions of theetalon, Ti, . . . T_(N). FP etalon 108 is exemplarily located along acommon optical axis in front of an imaging lens module, while imagesensor 104 is located at an imaging plane that coincides with a backfocal plane.

A spectral imaging system such as system 100 can provide N differentbroad-band images which are taken at different FP etalon states(operation modes).

System 100 can include or be otherwise operatively connected to aprocessing device (including for example a hardware processor such as aCPU, an FPGA, an ASIC, an image processor, and the like) configured toexecute the operations related to generating narrow band images frombroad band images as disclosed herein. According to one example, theprocessing device is part of control unit 106. According to anotherexample, the processing device is part of etalon 108. According to yetanother example, the processing unit is part of some other computerizeddevice externally connected to system 100

FIGS. 2A and 2B show two halves of the broad-band system responseobtained at different states of operation of the FP etalon and using acolor image sensor (e.g. with a Bayer RGB CFA).

The Bayer RGB CFA includes red pixels, blue pixels and green pixels. Ared pixel includes (or is preceded by) by a red filter, a green pixelincludes (or is preceded by) a green filter, and a blue pixel includes(or is preceded by) a blue filter.

Assuming that the FB etalon has N states then a red pixel is associatedwith N different transfer functions that are associated with (a) thetransfer function of the red filter and (b) the N different states ofthe FB etalon.

Assuming that the FB etalon has N states then a green pixel isassociated with N different transfer functions that are associated with(a) the transfer function of the green filter and (b) the N differentstates of the FB etalon.

Assuming that the FB etalon has N states then a blue pixel is associatedwith N different transfer functions that are associated with (a) thetransfer function of the blue filter and (b) the N different states ofthe FB etalon.

The spectral response is also represented by {acute over (H)}, see Eq.(4) below. The example illustrated in these figures shows 60 spectralbands obtained with N=20 etalon states. Each etalon state may have adifferent spectral response, marked as R1, R2, . . . R20, G1, G2, . . .G20 and B1, B2, . . . and B20.

The broad-band and asymmetrical system response (spectral transmission)contrasts with the response of an ideal hyperspectral filter thatprovides a narrow spectrum (e.g. with FWHM<50 nm) and substantiallysymmetrical band spectral response.

As mentioned, the present inventors have determined that the broad-bandasymmetric transmission curves of FIGS. 2A and 2B may be converted intorelatively narrow-band transmission curves (referred to hereinafter as“hyperspectral transmission curves” or “hyperspectral bands”) in anextended wavelength range (e.g. 400-1000 nm.

When the broad-band transmission curves are obtained with a color imagesensor, then N broad-band spectral images obtained in respective N FabriPerot etalon states of the spectral imager may be processed to providemore than N intermediate broad-band images.

A non-limiting example of an expansion process that is used to generatemore than N intermediate broad-band images is the demosaicing process.This is merely a non-limiting example and other expansion processes thatdiffer from the demosaicing process may be used to generate more than Nintermediate broad-band images. The expansion process may use anyextrapolation, interpolation, estimation or evaluation operations.

For simplicity of explanation the following examples will refer anexpansion process that is a demosaicing process.

The demosaicing algorithm may be used to reconstruct all color channelsin full resolution. The methods disclosed herein are applicable to allknown CFAs. For example, for an RGB Bayer CFA, a demosaicing algorithmmay be applied as follows: for each pixel of an image Í_(k) with indices[m, n], reconstruct the red pixel, the green pixel and the blue pixelsof corresponding red image, green image and blue image as a function ofthe neighboring pixels values (up to 2 pixels away in each direction inthe acquired image).

In the following example of a demosaicing process applies differentfunctions (fR for the red image, fG for the green image, and fB for theblue image) of sets of five by five adjacent pixels to generate thedifferent images.

Pixels of the red image are denoted I_(3k−2)[m, n].

Pixels of the green image are denoted I_(3k−1)[m, n].

Pixels of the blue image are denoted I_(3k) [m, n].I _(3k−2)[m,n]=Í _(k)[m,n]. R=f _(R)(Í _(k)[m−2:m+2,n−2:n+2])I _(3k−1)[m,n]=Í _(k)[m,n]. G=f _(G)(Í[m−2:m+2,n−2:n+2])I _(3k)[m,n]=Í _(k)[m,n]. B=f _(B)(Í[m−2:m+2,n−2:n+2])  (1)

In this case, the total number of images triples and is equal to{circumflex over (N)}=3N. In general, for CFAs having more than threedistinct colors, e.g. RGB-IR or RGBW CFAs, the total number of imagesafter demosaicing is equal to {circumflex over (N)}=cN

This is true for CFA having any number of c distinct colors, includingtwo or three. It should be noted that the CFA may be sensitive to two ormore frequency ranges—and that the frequency ranges may be visible colorfrequency ranges and/or may include at least one non-visible frequencyrange (for example—infrared, near IR and the like.). For a monochromatic(without CFA) sensor, I_(k)=Í_(k) and the total number of images N ispreserved.

A “spectral cube” is obtained, including set of images defined by twospatial coordinates and a third coordinate determined by the state ofthe FP etalon and the color channel. The goal is to transform thespectral cube into a hyperspectral cube such that the third coordinatecorrelates with a wavelength of a narrow-band filter.

In the general case (e.g. monochromatic sensors or sensors with anyCFA), for each state k of the FP etalon, the corresponding systemsignal, Í_(k), is given by:Í _(k)[m,n]={acute over (H)} _(k) R+ń _(k)[m,n]  (2)where R (size M×1) is the discretization of the radiosity (i.e. theinflux of photons on the image sensor) of the object, ń_(k) is the“noise” at each gap and {acute over (H)}_(k) (size 1×M) is thediscretization of the transmission spectrum at each gap of the etalongiven by:{acute over (H)} _(1×M)(k)=(T)(gap_(k),λ₁) . . . T(gap_(k),λ_(M)))  (3)where T (gap_(k), λ₁) is the transmission of the equivalent filter atgap k, in vicinity of wavelength λ₁. Matrix {acute over (H)}, which isthe total response of the system, is given by:

$\begin{matrix}{\overset{\prime}{H} = \begin{pmatrix}{T\left( {{gap}_{1},\lambda_{1}} \right)} & \ldots & {T\left( {{gap}_{1},\lambda_{M}} \right)} \\\vdots & \ddots & \vdots \\{T\left( {{gap}_{N},\lambda_{1}} \right)} & \ldots & {T\left( {{gap}_{N},\lambda_{M}} \right)}\end{pmatrix}} & (4)\end{matrix}$In {acute over (H)}_(N×M), N≥M, i. e. the number of etalon states isequal to or larger than the number of discrete wavelengths. It isassumed that the noise ń is only a weak function of R, i.e. ń=ń(λ_(i)).It should be noted that other assumptions about the noise may be used.

In the case of a color sensor, the previously described demosaicingprocedure (given by eq. (1) and shall be defined henceforth by D{Í}) (orany other process that may be used to generate many broad-band images)is applied to the system signal:I _(3N×1) =D{Í _(N×1) }=D{{acute over (H)} _(N×M) R _(M×1) +ń _(N×1) }=H_(3N×M) R _(M×1) +n _(3N×1)   (5a)where H_(3N×M)

D{{acute over (H)}_(N×M)} is the result of applying the demosaicingfunction to the total response function of the system, {acute over (H)},and is now a function of both gap and color channel (e.g. of R1, R2 . .. , G1, G2, . . . , B1, B2 . . . in FIGS. 2A and 2B).

For CFAs having c>1 distinct colors:I _(cN×1) =D{Í _(N×1) }=D{{acute over (H)} _(N×M) R _(M×1) +ń _(N×1) }=H_(cN×M) R _(M×1) +n _(cN×1)   (5b)For the monochromatic sensor case, the symbol H used henceforth issimply H_(N×M)={acute over (H)}_(N×M). H_(N×M).

The object radiosity R is estimated exemplarily by a reconstructionmatrix Ĥ_(inv) such that:{tilde over (R)}=Ĥ _(inv) I  (6)

When reconstructing the object radiosity R, it should be remembered thatfor most cases the noise has a Gaussian statistical distribution, thusthe maximum likelihood estimator {tilde over (R)} for R coincides with aleast square estimator which minimizes ∥I−HR∥₂ ² over R.

According to some non-limiting examples a cost function can be used asfollows:∥I−HR∥ ₂ ²+Regularization_term(σ,R)  (7)In which the second term is some general regularization function with σbeing some tuning parameter that is potentially by itself a function ofwavelength.The regularization term could be constructed to impose somecharacteristics on the reconstructed signal, e.g. smoothness of thesignal. It may be exemplarily derived based on the required spectralresolution and signal-to-noise ratio (SNR) per each wavelength λ.

-   For example, using Tikhonov's regularization method, the following    cost function in which Γ is some suitably chosen Tikhonov matrix may    be used for minimization:    ∥{acute over (H)} _(inv) HR−R∥ ₂ ² +∥ΓR∥ ₂ ²  (8)    The solution to the problem of minimizing this cost function is then    given by:    {tilde over (R)}=(H ^(T) H+Γ ^(T)Γ)⁻¹ H ^(T) I  (9)    and thus:    Ĥ _(inv)=(H ^(T) H+Γ ^(T)Γ)⁻¹ H ^(T)  (10)

Tikhonov's matrix Γ could be chosen, for example, as some multiple α ofthe identity matrix (Γ=αI), giving preference to solutions with smallernorms, which is known as the L2 type regularization. Alternatively,since the object radiosity R is assumed to be continuous, Γ could beconstructed as some lowpass operator (e.g. a difference operator or aweighted Fourier operator) which enforces smoothness on thereconstructed {tilde over (R)}.

For any choice of Γ, the system performance may then be assessed interms of the resulting resolution and the SNR. By assigning differentweights to these parameters, an optimal Γ may be constructed.

For example, by sweeping through values of a in a certain predeterminedrange, it is possible to create maps of the system's resolution and SNRvs. wavelength. The system's performance at each reconstructedwavelength as a function of α is assessed by a weighted sum of thesemaps. The optimization is then performed by choosing, for eachwavelength, a different value of α_(i) which minimizes the weighted sumat that wavelength. In this case α is in fact a diagonal matrixα=diag(α_(i)) multiplying the Tikhonov operator matrix {tilde over (Γ)}such that: Γ=α{tilde over (Γ)}.

According to another non-limiting example, when choosing areconstruction matrix Ĥ_(inv), goal can be set, for example, to minimizethe magnitude of the following cost function:∥{tilde over (R)}−R∥ ₂ =∥Ĥ _(inv) I−R∥ ₂ ≤∥Ĥ _(inv) HR−R∥ ₂ +∥Ĥ _(inv)n∥ ₂  (11)

The first term (Ĥ_(inv)HR−R∥₂) on the right-hand side of this expression(data term) accounts for the deviations of the reconstruction.Minimizing this term is equivalent to minimizing its square, which isoften more convenient to use for calculations. It is beneficial for thetotal system response Ĥ_(inv)H to resemble an ideal narrow-band (e.g.hyperspectral) filter, independently of the object radiosity. By usingcompatibility of induced norms, the following could be said about thedata term in eq. (11):∥R−Ĥ _(inv) HR∥ ₂ ²≤∥Identity_(M×M) −Ĥ _(inv) H∥ ₂ ∥R∥ ₂  (12)Where Identity_(M×M) is the identity matrix of size M×M.

With a possible goal of limiting noise amplification, e.g. ∥Ĥ_(inv)∥₂²<σ, the following cost function could be used in this exemplary method:∥Identity_(M×M) −Ĥ _(inv) H∥ ₂ ²+Regularization_term(σ,Ĥ _(inv))  (13)As previously, here σ is some tuning parameter, which may be constructedas a function of wavelength. This general regularization term could beconstructed to impose some characteristics on the reconstructed signal,e.g., noise amplification, or smoothness of the signal. Theregularization term may be exemplarily derived based on the requiredspectral resolution and signal-to-noise ratio (SNR) per each wavelengthλ.Since using an identity matrix poses a very strict requirement on theminimization, a general matrix O_(M×M) might be used instead and thegeneral cost function is written as:∥O _(M×M) −Ĥ _(inv) H∥ ₂ ²+Regularization_term(σ,Ĥ _(inv))  (14)In this minimization problem, the FWHM of the rows of matrix O in factrepresents the reconstruction spectral resolution.

As exemplified before, using Tikhonov's regularization method, thefollowing cost function in which Γ is some suitably chosen Tikhonovmatrix may be used for this minimization:∥O _(M×M) ^(T) −H ^(T) Ĥ _(inv) ^(T)∥₂ ² +∥ΓĤ _(inv) ^(T)∥₂ ²  (15)Here, the fact that an L2 norm of a matrix is equivalent to the norm ofits transpose was used. The solution to the problem of minimizing thiscost function is then given by:Ĥ _(inv) =O ^(T) H[(H ^(T) H+Γ ^(T)Γ)⁻¹]^(T)  (16)

In addition to the examples mentioned above, various regression methodsmay be implemented to estimate the spectral bands of the image, bothlinear and nonlinear.

Furthermore, various methods other than regression such as machinelearning, neural network or artificial intelligence methods may beimplemented to estimate the object radiosity R.

The mentioned algorithms could be tuned for any specific applicationrequirements. It is noted that the required spectral resolution ofreconstruction can be tunable—and accordingly the number of broadbandimages, i.e. for different applications data would be pre-processed andprocessed differently. For example, different optimal reconstructionmatrices (Ĥ_(inv)) could be used for different SNR requirements.FIG. 8A shows an example of a system which includes a sensor and atunable filter between an object and the image sensor. The system'ssignal is Í_(k)[m, n]={acute over (H)}_(k)R+ń_(k)[m, n] in which R(λ_(i)) is the radiosity of the object's surface which can be estimated,for example, by the methods described thus far.The system can be enhanced, for example with a tunable light source, e.gled array or a white source with tunable filter. Such tunable lightsource may improve the results of the spectrum estimation, by refiningthe collected data and enhance the estimation.

FIG. 8B shows an example of a system that includes a sensor and atunable light source—without filter in front of the sensor. The tunablelight source can either comprise an array of LEDs (or other types oflight sources), each illuminating at a different wavelength band, or abroad-band light source with a tunable filter in front of it (asexemplified in the figure). In either case, the methods forreconstructing the object's radiosity are practically identical to themethods discussed thus far. Furthermore, this still enables to use thesame methods to get narrower bands relative to the original light sourcebands.

Assuming that the emissivity of the surface of an object is ε(λ_(i)),then the radiosity of the object's surface is {acute over (H)}_(k)Eε inwhich {acute over (H)}_(k) relates to the tunable filter's response,E(λ_(i)) is the pre-filtered light source intensity, and {acute over(H)}_(k)E is the irradiance on the object's surface. In case of an arrayof LEDs (or other types of light sources) it is still possible to writeirradiance on the object's surface as {acute over (H)}_(k)E. Followingthe exemplary methods described thus far, the object's spectral responsecan be estimated from the system's signal Í_(k)[m, n]={acute over(H)}_(k)R+ń_(k)[m, n] in which R is defined as R=Eε.

FIG. 8C shows another example of a system which is a combination of theexamples in FIGS. 8A-B and includes a tunable light source (as describedabove) with an additional tunable filter in front of the image sensor.In this example, R=Eε and the total response of the filters is {acuteover (H)}_(k)={acute over (H)}_(2,k2){acute over (H)}k_(1,k1) in which{acute over (H)}_(1,k1) is the response of the filter in front of thelight source set at gap k₁ and {acute over (H)}_(2,k2) is the responseof the filter in front of the image sensor set at gap k₂.

In this case, it is possible to obtain narrow band images solely byalternating the filter and the light source spectra. In this method, thelight that reaches the sensor will include only the common wavelengthstransmittable by both filters at their set gaps.

In a more concise manner, FIG. 3 shows schematically in a flow chart thetwo general steps of a method disclosed herein: in step 300, a series ofbroad-band spectral images of an object is acquired by operating thetunable FP etalon in a series of sequential states. In step 302, thebroad-band spectral images are processed into narrower band images.

Step 302 may be followed by a step of—using the narrow band images e.g.displaying one or more of the images (for example—one image at a time)on a computer display device, storing one or more of the images,transmitting one or more of the images, and the like—or some otherusage.

FIG. 4A shows schematically in a flow chart more details of a method.

In step 400, N broad-band spectral images Í_(1 . . . N) are acquired. Instep 402, a demosaicing algorithm is applied on the N broad-bandspectral images to reconstruct all color channels in full resolution,thereby obtaining cN broad-band spectral images (e.g. 3N when C=3 for aBayer CFA) or 4N broad-band spectral images (where C=4 when using RGB-IRor RGBW CFAs).

In step 404, a series of narrow-band spectral images, {tilde over(R)}_(1 . . . M), is constructed by linearly transformingI_(1 . . . {circumflex over (N)}) using the matrix

${{{\overset{\hat{}}{H}}_{inv}:\begin{pmatrix}{\overset{˜}{R}}_{1} \\\vdots \\{\overset{˜}{R}}_{M}\end{pmatrix}} = {{\overset{\hat{}}{H}}_{inv}\begin{pmatrix}I_{1} \\\vdots \\I_{\hat{N}}\end{pmatrix}}},{\overset{\hat{}}{N} = {cN}},{M \leq {{cN}.}}$

FIG. 4B shows schematically in a flow chart more details of a methodaccording to an example disclosed herein, for a FP etalon based spectralimager with a monochromatic image sensor. In step 410, N broad-bandspectral images I_(1 . . . N) are acquired. In step 412, a series ofnarrow-band spectral images, {tilde over (R)}_(1 . . . M), isconstructed by linearly transforming I_(1 . . . N) using the matrix

${{{\overset{\hat{}}{H}}_{inv}:\begin{pmatrix}{\overset{˜}{R}}_{1} \\\vdots \\{\overset{˜}{R}}_{M}\end{pmatrix}} = {{\overset{\hat{}}{H}}_{inv}\begin{pmatrix}I_{1} \\\vdots \\I_{N}\end{pmatrix}}},{M \leq {N.}}$

FIGS. 5A-5C show a “modified” total system response Ĥ_(inv)H in threeseparate graphs. The “modified” term refers to the fact that the totalsystem response is changed from the response shown in FIGS. 2A and 2B asa result of the processing applied in the methods described above. Eachgraph provides a number of narrow band HHi curves (spectra).

In summary, the present inventors have managed to perform narrow-bandspectral imaging and even hyperspectral imaging using a FP etalon-basedspectral imager that was not known to be able to provide such spectralor hyperspectral imaging.

FIG. 6 illustrates an example of a method 600, according to thepresently disclosed subject matter. Some operations described below withreference to FIG. 6 (as well as FIG. 7 and FIGS. 3, 4 a and 4 bdescribed above) can be performed by a processing circuitry configuredfor this purpose. As mentioned above such processing circuitry can bepart of system 100 (e.g. as part of control unit 106 and/or etalon 108)or according to other examples be part of a computerized deviceexternally connectable to system 100.

Method 600 may involve generating narrow-band spectral images.

Method 600 may include steps 610 and 620.

Step 610 may include acquiring, by a spectral imager that comprises atunable filter, a first plurality (N) of broad-band spectral imagesassociated with respective states of the tunable filter. N is an integerthat exceeds one. The tunable filter may be a Fabri-Perot tunable filtersuch as a MEMS Fabri-Perot etalon (as shown above by way of example withreference to FIG. 1 ). The respective states of the tunable filter mayinclude N different states. The respective states differ from each otherby their transfer function.

Step 610 may be followed by step 620 of processing, by a processingcircuitry (such as a hardware processor)), the first plurality ofbroad-band spectral images into a second plurality (M) of narrow-bandspectral images. M is an integer that exceeds one. The processing mayinclude executing instructions and/or code by the processing circuitry.

The processing circuitry may be a central processing unit, a graphicprocessor, a hardware accelerator, an FPGA, an ASIC, and the like.

The spectral imager may include an image sensor that may be amonochromatic sensor or a color filter that has a third plurality (C) offilter types. filters of different types differ from each other bytransfer function. C is an integer than exceeds two.

The image sensor may include any combination of any number of filtertypes—for example—(a) red, green and blue, (b) red, green, blue andwhite, (c) red, green, blue and infrared, (d) red, blue and white, andthe like.

Step 620 may include step 622 of applying an expansion process forgenerating, from the first plurality of broad-band spectral images, afourth plurality (Q) of broad-band spectral images. Q is a positiveinteger. Q exceeds N. Q exceeds M. The ratio between Q and N may be aninteger or not.

The expansion process increases the amount of information. The expansionprocess may be a demosaicing process but may differ from a demosaicingprocess.

Step 622 may be followed by step 624 of processing the fourth pluralityof broad-band spectral images into the second plurality of thenarrow-band spectral images.

Step 624 may include constructing the second plurality of narrow-bandspectral images by linearly transforming the fourth plurality ofbroad-band spectral images using a reconstruction matrix.

Examples of calculations that are executed during step 624 areillustrated in the pages above—especially equations (1)-(10) and theassociated text.

Step 624 may include constructing the second plurality of narrow-bandspectral images by using a reconstruction matrix; wherein thereconstruction matrix represents a cost function and spectral responsesassociated with respective states of the tunable filter. Thereconstruction matrix may be calculated based on a Tikhonov matrix. TheTikhonov matrix may be a multiple (alpha) of the identity matrix.

The Tikhonov matrix may be selected out of a group of Tikhonov matrices.See, for example, the selection of alpha.

The group of Tikhonov matrices may be associated with a group ofreconstruction matrices. Different reconstruction matrices of the groupmay be associated with different values of one or more spectral imagerperformance attributes. The one or more spectral imager performanceattributes may be signal to noise ratio and/or resolution.

Step 624 may include calculating the reconstruction matrix.

Step 624 may include selecting the Tikhonov matrix out of a group ofTikhonov matrices.

According to one example, the calculation or selection of thereconstruction matrices (e.g. Tikhonov matrices) may be executed beforegenerating the fourth plurality of broad-band spectral images. Accordingto another example, the calculation or selection may be executed aftergenerating the fourth plurality of broad-band images but beforeprocessing the fourth plurality of broad-band spectral images into thesecond plurality of the narrow-band spectral images. According to yetanother example, the calculation or selection may be executed during theprocessing of the fourth plurality of broad-band spectral images intothe second plurality of the narrow-band spectral images.

The selection may be based on at least one property of at least one ofthe first plurality of broad-band spectral images.

Accordingly—after one or more broad-band spectral images are acquiredduring step 610—the method may evaluate one or more property and thendecide which Tikhonov matrix to select. For example—assuming that afirst broad-band spectral image is acquired and has a low signal tonoise ratio then a Tikhonov matrix that is associated with low signal tonoise ratio should be selected. In this example there may be a need toincrease the signal to noise ratio of one or more narrow-band spectralimages generated during step 620—and more emphasis may be assigned tothe signal to noise ratio.

FIG. 7 illustrates an example of method 700.

Method 700 may involve generating narrow-band spectral images.

Method 700 may include steps 610 and 621.

Step 610 may include acquiring, by a spectral imager that comprises atunable filter, a first plurality (N) of broad-band spectral imagesassociated with respective states of the tunable filter. N is an integerthat exceeds one. The tunable filter may be a Fabri-Perot tunable filtersuch as a MEMS Fabri-Perot etalon. The respective states of the tunablefilter may include N different states. The respective states differ fromeach other by their transfer function.

Step 610 may be followed by step 621 of processing, by a processingcircuitry, the first plurality of broad-band spectral images into asecond plurality (M) of narrow-band spectral images. M is an integerthat exceeds one.

Step 621 differs from step 620 by including step 626 instead of steps622 and 624. Notably, step 621 does not include performing the expansionprocess.

Step 626 may include constructing the second plurality of narrow-bandspectral images by linearly transforming the first plurality ofbroad-band spectral images using a reconstruction matrix.

Step 626 may include constructing the second plurality of narrow-bandspectral images by using a reconstruction matrix; wherein thereconstruction matrix represents a cost function and spectral responsesassociated with respective states of the tunable filter. Thereconstruction matrix may be calculated based on a Tikhonov matrix. TheTikhonov matrix may be a multiple (alpha) of the identity matrix.

The Tikhonov matrix may be selected out of a group of Tikhonov matrices.See, for example, the selection of alpha described above.

The group of Tikhonov matrices may be associated with a group ofreconstruction matrices. Different reconstructions matrices of the groupmay be associated with different values of one or more spectral imagerperformance attributes. The one or more spectral imager performanceattributes may be signal to noise ratio and/or resolution.

Step 626 may include calculating the reconstruction matrix.

Step 626 may include selecting the Tikhonov matrix out of a group ofTikhonov matrices.

The selecting may be executed during the processing of the firstplurality of broad-band spectral images into the second plurality of thenarrow-band spectral images.

The selection may be based on at least one property of at least one ofthe first plurality of broad-band spectral images.

The various features and steps discussed above, as well as other knownequivalents for each such feature or step, can be mixed and matched byone of ordinary skill in this art to perform methods in accordance withprinciples described herein. Although the disclosure has been providedin the context of certain embodiments and examples, it will beunderstood by those skilled in the art that the disclosure extendsbeyond the specifically described embodiments to other alternativeembodiments and/or uses and obvious modifications and equivalentsthereof. Accordingly, the disclosure is not intended to be limited bythe specific disclosures of embodiments herein.

For example, any digital computer system can be configured or otherwiseprogrammed to implement a method disclosed herein, and to the extentthat a particular digital computer system is configured to implementsuch a method, it is within the scope and spirit of the disclosure. Oncea digital computer system is programmed to perform particular functionspursuant to computer-executable instructions from program software thatimplements a method disclosed herein, it in effect becomes a specialpurpose computer particular to an embodiment of the method disclosedherein. The techniques necessary to achieve this are well known to thoseskilled in the art and thus are not further described herein. Themethods and/or processes disclosed herein may be implemented as acomputer program product such as, for example, a computer programtangibly embodied in an information carrier, for example, in anon-transitory computer-readable or non-transitory machine-readablestorage device and/or in a propagated signal, for execution by or tocontrol the operation of, a data processing apparatus including, forexample, one or more programmable processors and/or one or morecomputers. The term “non-transitory” is used to exclude transitory,propagating signals, but to otherwise include any volatile ornon-volatile computer memory technology suitable to the applicationincluding, for example, distribution media, intermediate storage media,execution memory of a computer, and any other medium or device capableof storing for later reading by a computer program implementingembodiments of a method disclosed herein. A computer program product canbe deployed to be executed on one computer or on multiple computers atone site or distributed across multiple sites and interconnected by acommunication network.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

Unless otherwise stated, the use of the expression “and/or” between thelast two members of a list of options for selection indicates that aselection of one or more of the listed options is appropriate and may bemade.

It should be understood that where the claims or specification refer to“a” or “an” element, such reference is not to be construed as therebeing only one of that element.

It is appreciated that certain features of the invention, which are, forclarity, described in the context of separate embodiments or example,may also be provided in combination in a single embodiment. Conversely,various features of the invention, which are, for brevity, described inthe context of a single embodiment, may also be provided separately orin any suitable sub-combination or as suitable in any other describedembodiment of the invention. Certain features described in the contextof various embodiments are not to be considered essential features ofthose embodiments, unless the embodiment is inoperative without thoseelements.

All patents and patent applications mentioned in this application arehereby incorporated by reference in their entirety for all purposes setforth herein. It is emphasized that citation or identification of anyreference in this application shall not be construed as an admissionthat such a reference is available or admitted as prior art.

The terms “including”, “comprising”, “having”, “consisting” and“consisting essentially of” are used in an interchangeable manner. Forexample—any method may include at least the steps included in thefigures and/or in the specification, only the steps included in thefigures and/or the specification. The same applies to the spectralimager and the mobile computer.

It will be appreciated that for simplicity and clarity of illustration,elements shown in the figures have not necessarily been drawn to scale.For example, the dimensions of some of the elements may be exaggeratedrelative to other elements for clarity. Further, where consideredappropriate, reference numerals may be repeated among the figures toindicate corresponding or analogous elements.

In the foregoing specification, the invention has been described withreference to specific examples of embodiments of the invention. It will,however, be evident that various modifications and changes may be madetherein without departing from the broader spirit and scope of theinvention as set forth in the appended claims.

Moreover, the terms “front,” “back,” “top,” “bottom,” “over,” “under”and the like in the description and in the claims, if any, are used fordescriptive purposes and not necessarily for describing permanentrelative positions. It is understood that the terms so used areinterchangeable under appropriate circumstances such that theembodiments of the invention described herein are, for example, capableof operation in other orientations than those illustrated or otherwisedescribed herein.

Those skilled in the art will recognize that the boundaries betweenlogic blocks are merely illustrative and that alternative embodimentsmay merge logic blocks or circuit elements or impose an alternatedecomposition of functionality upon various logic blocks or circuitelements. Thus, it is to be understood that the architectures depictedherein are merely exemplary, and that in fact many other architecturescan be implemented which achieve the same functionality.

Any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality can be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermedial components. Likewise, any two components soassociated can also be viewed as being “operably connected,” or“operably coupled,” to each other to achieve the desired functionality.

Furthermore, those skilled in the art will recognize that boundariesbetween the above described operations merely illustrative. The multipleoperations may be combined into a single operation, a single operationmay be distributed in additional operations and operations may beexecuted at least partially overlapping in time. Moreover, alternativeembodiments may include multiple instances of a particular operation,and the order of operations may be altered in various other embodiments.

Also for example, in one embodiment, the illustrated examples may beimplemented as circuitry located on a single integrated circuit orwithin a same device. Alternatively, the examples may be implemented asany number of separate integrated circuits or separate devicesinterconnected with each other in a suitable manner.

Also for example, the examples, or portions thereof, may implemented assoft or code representations of physical circuitry or of logicalrepresentations convertible into physical circuitry, such as in ahardware description language of any appropriate type.

Also, the invention is not limited to physical devices or unitsimplemented in non-programmable hardware but can also be applied inprogrammable devices or units able to perform the desired devicefunctions by operating in accordance with suitable program code, such asmainframes, minicomputers, servers, workstations, personal computers,notepads, personal digital assistants, electronic games, automotive andother embedded systems, cell phones and various other wireless devices,commonly denoted in this application as ‘computer systems’.

However, other modifications, variations and alternatives are alsopossible. The specifications and drawings are, accordingly, to beregarded in an illustrative rather than in a restrictive sense.

In the claims, any reference signs placed between parentheses shall notbe construed as limiting the claim. The word ‘comprising’ does notexclude the presence of other elements or steps then those listed in aclaim. Furthermore, the terms “a” or “an,” as used herein, are definedas one as or more than one. Also, the use of introductory phrases suchas “at least one” and “one or more” in the claims should not beconstrued to imply that the introduction of another claim element by theindefinite articles “a” or “an” limits any particular claim containingsuch introduced claim element to inventions containing only one suchelement, even when the same claim includes the introductory phrases “oneor more” or “at least one” and indefinite articles such as “a” or “an.”The same holds true for the use of definite articles. Unless statedotherwise, terms such as “first” and “second” are used to arbitrarilydistinguish between the elements such terms describe. Thus, these termsare not necessarily intended to indicate temporal or otherprioritization of such elements the mere fact that certain measures arerecited in mutually different claims does not indicate that acombination of these measures cannot be used to advantage.

Any system, apparatus or device referred to this patent applicationincludes at least one hardware component.

While certain features of the invention have been illustrated anddescribed herein, many modifications, substitutions, changes, andequivalents will now occur to those of ordinary skill in the art. It is,therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the invention.

Any combination of any component of any component and/or unit ofspectral imager that is illustrated in any of the figures and/orspecification and/or the claims may be provided.

Any combination of any spectral imager illustrated in any of the figuresand/or specification and/or the claims may be provided.

Any combination of any set of spectral imagers illustrated in any of thefigures and/or specification and/or the claims may be provided.

Any combination of steps, operations and/or methods illustrated in anyof the figures and/or specification and/or the claims may be provided.

Any combination of operations illustrated in any of the figures and/orspecification and/or the claims may be provided.

Any combination of methods illustrated in any of the figures and/orspecification and/or the claims may be provided.

While this disclosure has been described in terms of certain embodimentsand generally associated methods, alterations and permutations of theembodiments and methods will be apparent to those skilled in the art.The disclosure is to be understood as not limited by the specificembodiments described herein, but only by the scope of the appendedclaims.

What is claimed is:
 1. A method of generating narrow-band spectralimages, the method comprising: acquiring, by a spectral imager thatcomprises a tunable filter, a first plurality (N) of broad-band spectralimages, each is acquired while the tunable filter is at a differentstate; and processing, by a hardware processor, the first plurality ofbroad-band spectral images, the processing comprising: applying areconstruction matrix that represents a cost function and spectralresponses associated with different states of the tunable filter on theplurality of broad-band spectral images to thereby construct a secondplurality (M) of narrow-band spectral images and improve spectralresolution of the spectral images.
 2. The method according to claim 1,wherein each broad-band image of the first plurality of broad-bandspectral images is associated with a respective broad-band transmissioncurve having a respective broad-band full width half maximum value; andwherein each narrow-band spectral image of the second plurality ofnarrow-band spectral images is associated with a respective narrow-bandtransmission curve having a narrow-band full width half maximum smallerthan the broad-band full width half maximum value of the broad-bandtransmission curve.
 3. The method of claim 2, wherein the spectralimager includes an image sensor having a filter array with a thirdplurality (C) of filter types, wherein filters of different types differfrom each other by transfer function; and wherein C exceeds two.
 4. Themethod of claim 3, wherein C equals three and the filter array is anyone of: a color filter array; a red, green, and blue color filter array;and a red, blue and white filter array.
 5. The method of claim 3,wherein C equals four and the filter array is any one of: a red, green,blue, and infrared filter array; and a red, green, blue and white filterarray.
 6. The method of claim 3, wherein the method comprises applyingan expansion process for generating, from the first plurality ofbroad-band spectral images, a fourth plurality (Q) of broad-bandspectral images and processing the fourth plurality of broad-bandspectral images into the second plurality of the narrow-band spectralimages; and wherein Q exceeds each one of N and M.
 7. The methodaccording to claim 6, wherein a ratio between Q and N is an integer. 8.The method according to claim 6, wherein the expansion process is ademosaicing process.
 9. The method of claim 6, wherein the processing ofthe fourth plurality of broad-band spectral images into the secondplurality of narrow-band spectral images comprises constructing thesecond plurality of narrow-band spectral images by linearly transformingthe fourth plurality of broad-band spectral images using areconstruction matrix.
 10. The method according to claim 1, wherein thereconstruction matrix is calculated based on a Tikhonov matrix.
 11. Themethod according to claim 10, wherein the Tikhonov matrix is a multipleof the identity matrix.
 12. The method according to claim 10, whereinthe Tikhonov matrix is a lowpass operator.
 13. The method according toclaim 10, wherein the Tikhonov matrix is selected out of a group ofTikhonov matrixes, the group of Tikhonov matrixes are associated with agroup of reconstruction matrixes; wherein different reconstructionsmatrixes of the group are associated with different values of one ormore spectral imager performance attributes and wherein the one or morespectral imager performance attributes comprises any one of: signal tonoise ratio; resolution.
 14. The method according to claim 1, whereinthe reconstruction matrix equals: (H^(t)H+V^(T)Vy¹H^(T)), wherein H is amatrix that represents spectral responses associated with respectivestates of the tunable filter, and T a Tikhonov matrix.
 15. The methodaccording to claim 10, comprising selecting the Tikhonov matrix out of agroup of Tikhonov matrixes based on at least one property of at leastone of the first plurality of broad-band spectral images, wherein the atleast one property is selected from: signal to noise ratio; andresolution.
 16. The method according to claim 1, wherein the firstplurality (N) of broad-band spectral images is acquired by amonochromatic image sensor.
 17. The method according to claim 1, whereinthe tunable filter is a Fabri Perot etalon and wherein each state of thetunable filter correspond to a different gap between reflective surfacesof the tunable filter.
 18. The method according to claim 1, wherein atransmission curve of each state partially overlaps the transmissioncurves of neighboring states.
 19. A spectral imager that comprises atunable filter and an image sensor; wherein the sensor is configured toacquire a first plurality (N) of broad-band spectral images, each isacquired while the tunable filter is at a different state; and theimager further comprise a processor configured to process the firstplurality of broad-band spectral images, the processing comprising:applying a reconstruction matrix that represents a cost function andspectral responses associated with different states of the tunablefilter on the plurality of broad-band spectral images to therebyconstruct a second plurality (M) of narrow-band spectral images andimprove spectral resolution of images provided by the imager.
 20. Thespectral imager according to claim 19, wherein each broad-band image ofthe first plurality of broad-band spectral images is associated with arespective broad-band transmission curve having a respective broad-bandfull width half maximum value; and wherein each narrow-band spectralimage of the second plurality of narrow-band spectral images isassociated with a respective narrow-band transmission curve having anarrow-band full width half maximum smaller than the broad-band fullwidth half maximum value of the broad-band transmission curve.
 21. Thespectral imager according to claim 19, wherein the image sensor includesa filter array with a third plurality (C) of filter types, whereinfilters of different types differ from each other by transfer function;and wherein C exceeds two.
 22. The spectral imager according to claim21, wherein C equals three and the filter array is any one of: a colorfilter array; a red, green, and blue color filter array; and a red,blue, and white filter array.
 23. The spectral imager according to claim21, wherein C equals four and the filter array is any one of: red,green, blue, and infrared filter array and a red, green, blue, and whitefilter array.
 24. The spectral imager according to claim 21, wherein theprocessor is configured to apply an expansion process for generating,from the first plurality of broad-band spectral images, a fourthplurality (Q) of broad-band spectral images and process the fourthplurality of broad-band spectral images into the second plurality of thenarrow-band spectral images; and wherein Q exceeds each one of N and M.25. The spectral imager according to claim 24, wherein a ratio between Qand N is an integer.
 26. The spectral imager according to claim 24,wherein the processor is configured to construct the second plurality ofnarrow-band spectral images by linearly transforming the fourthplurality of broad-band spectral images using a reconstruction matrix.27. The spectral imager according to claim 19, wherein thereconstruction matrix is calculated based on a Tikhonov matrix.
 28. Thespectral imager according to claim 19, wherein the image sensor is amonochromatic image sensor.
 29. The spectral imager according to claim19, wherein the tunable filter is a Fabri Perot etalon, and wherein eachstate of the tunable filter corresponds to a different gap betweenreflective surfaces of the tunable filter.
 30. The spectral imageraccording to claim 19, wherein a transmission curve of each statepartially overlaps the transmission curves of neighboring states.
 31. Anon-transitory computer readable storage medium tangibly embodying aprogram of instructions that, when executed by a computer, causing thecomputer to perform a method of generating narrow-band spectral images,the method comprising: acquiring, by a spectral imager that comprises atunable filter, a first plurality (N) of broad-band spectral images,each is acquired while the tunable filter is at a different state; andprocessing, by a hardware processor, the first plurality of broad-bandspectral images, the processing comprising: applying a reconstructionmatrix that represents a cost function and spectral responses associatedwith different states of the tunable filter on the plurality ofbroad-band spectral images to thereby construct a second plurality (M)of narrow-band spectral images and improve spectral resolution of thespectral images.
 32. The non-transitory computer readable storage mediumaccording to claim 31, wherein a transmission curve of each statepartially overlaps the transmission curves of neighboring states.